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 A079715 a(n) = Pi(n) - Pi(sqrt(n)) + 1. 1

%I

%S 1,2,3,2,3,3,4,4,3,3,4,4,5,5,5,5,6,6,7,7,7,7,8,8,7,7,7,7,8,8,9,9,9,9,

%T 9,9,10,10,10,10,11,11,12,12,12,12,13,13,12,12,12,12,13,13,13,13,13,

%U 13,14,14,15,15,15,15,15,15,16,16,16,16,17,17,18,18,18,18,18,18,19,19,19,19

%N a(n) = Pi(n) - Pi(sqrt(n)) + 1.

%C a(n) = Sum( d' dividing n, mu(d')*floor(n/d')) where each prime factor of d' is <=sqrt(n).

%C A well-known application of the principle of inclusion-exclusion used in sieve methods.

%C Number of numbers less than or equal to n and coprime to the product of the primes less than sqrt(n), i.e., to A104588(n). - _Lekraj Beedassy_, Mar 17 2005

%H G. C. Greubel, <a href="/A079715/b079715.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = pi(n) - pi(sqrt(n)) + 1 = A000720(n) - A056811(n) + 1 = A056812(n) + 1.

%t Table[PrimePi[n] - PrimePi[Sqrt[n]] + 1, {n, 1, 100}] (* _G. C. Greubel_, May 13 2017 *)

%o (PARI) for(n=1,100, print1(primepi(n) - primepi(sqrt(n)) + 1, ", ")) \\ _G. C. Greubel_, May 13 2017

%Y Cf. A000720, A056811, A056812.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Feb 16 2003

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew Plewe_, Jun 12 2007

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